Question

Numerele a , b ,c sunt direct proportionale cu numerele : 0.25 , 0,(3) , so 0,5 si verifica relatia : 4(ab+bc+ca)=3abc . Aflati suma numerelor a , b , c .

Answer 1

{a.b.c}d.p{0,25,0,(3),0,5}
0,25=25/100 simplificam prin 25=1/4
0,(3)=3/9=1/3
0,5=50/100 simplificam prin 50=1/2
{a,b,c}d.p{1/4,1/3,1/2}=> a/1/4=b/1/3=c/1/2=>a=1/4k
                                                                              b=1/3k
                                                                              c=1/2k
4(ab+bc+ca)=3abc
4(1/4*1/3+1/3*1/2+1/2*1/4)=3*1/4*1/3*1/2)
4(3/12*4/12+4/12*6/12+6/12*3/4)=3*3/12*4/12*6/12)
4(12/12+24/12+18/12)=36/12*3/12*4/12*6/12)
4(36/12+18/12)=108/12*24/12
48/13*54/12=2592/12
2592/12k=2592/12k
216k=216k=>k=1
a=1/4
k=1=>a=1/4*1=1/4

b=1/3
k=1=>b=1/3*1=1/3

c=1/2
k=1=>c=1/2*1==1/2
a+b+c=1/4+1/3+1/2=
=3/12+4/12+6/12
=13/12 si asa ramane
coroana?am muncit mult.